2013/05/29 by Sergey Neshveyev, Makoto Yamashita, Neshveyev, Sergey +1
Mathematics · #17B37 (Primary) 18D10 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA #msc:17B37 #msc:18D10
paper · pdf · doi:10.48550/arxiv.1305.6949
20 pages; remark on braiding, minor modifications
openalex publication_date 2013/05/29 · arxiv created 2013/07/09 · arxiv updated 2013/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a compact semisimple Lie group G of rank r, and a parameter q>0, we can define new associativity morphisms in Rep(Gq) using a 3-cocycle Φ on the dual of the center of G, thus getting a new tensor category Rep(Gq)Φ. For a class of cocycles Φ we construct compact quantum groups Gτq with representation categories Rep(Gq)Φ. The construction depends on the choice of an r-tuple τ of elements in the center of G. In the simplest case of G=SU(2) and τ=-1, our construction produces Woronowicz's quantum group SU-q(2) out of SUq(2). More generally, for G=SU(n), we get quantum group realizations of the Kazhdan-Wenzl categories.